Now I want to do the following. I want to plot the points: $(-1,0),(1,0),(0,0),(x,0),(1, \pm 1),(1,\pm \frac{1}{\sqrt 3}),(0, \pm \frac{2}{\sqrt 3}),(0, \pm \sqrt 2)$ in this graphic. I'm able to plot points using Graphics[Point[{x, y}]but I would like to plot those point in the same graphic. This is probably really easy, but I can't find it in the documentation.

For fun, let's describe the ellipse--which is actually a circle--in polar coordinates and specify the points more simply as complex numbers rather than pairs of reals. And then use David Park's Presentations add-on (http://home.comcast.net/~djmpark/DrawGraphicsPage.html) in order to draw the whole thing--without having to use PlotStyle, Graphics, or Show (at least, not overtly):

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